how to derive the cross product formula: |u x v| = |u| x |v| sin (angle)

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A: The given vector is r→t=5t sint + 5costi^+5t cost + 5sintj^. To find: (a) unit tangent curve of the…

Q: The figure shows f, f', and f". Determine which is which. 2 y 0 -2 1

A: In this question we have to determine which is f, f' and f''.

Q: Find the angle θ between v = (3, 6, 2) and w = (4, 2, 4).

A: Given, v = (3, 6, 2) w = (4, 2, 4)

Q: The linear approximation at x = 0 to sin(9x) is A + Bx where A is: and where B is:

A: Given fx=sin9x Differentiate fx=sin9x with respect to x, we get f'x=ddxsin9x=9cos9x Hence,…

Q: Given f(x, y, z)=√x+6y-52, find fz(x, y, z)= 1₂(x, y, z)= f.(x, y, z)=

A: Partial Derivative

Q: Find the angle between u = i - 2j - 2k and v = 6i + 3j + 2k.

A:

Q: Consider the following vector-valued function: B: (π,0) × (0, 1) → R³, (a) Sketch the values of ß…

A:

Q: find the length and direction of (u x v) and (v x u) u = 21 -2j - k, v =i - k

A: Determine the cross product.…

Q: Consider the function f(x, y, z) = x² sin(yz). a) Calculate f-(x, y, z). fy(x, y, z), and f:(x, y,…

A:

Q: Find the real and imaginary parts u(x, y) and v(x, y) of the following functions. Use theCauchy-…

A: A) not analytic function